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We investigate the presence of logarithmic CFT doublets in the soft sector of celestial CFT related with supertranslations. We show that the quantum operator associated with a $\log u$ late-time behavior for the asymptotic gravitational shear forms a logarithmic CFT pair of conformal dimension $\Delta=1$ with an IR-regulated supertranslation Goldstone current. We discuss this result in connection with previous encounters of log CFT structures in the IR-finite part of celestial OPEs., Comment: 28 pages + appendices

Science communication aims at making key research insights accessible to the broad public. If explanatory and exploratory visualization techniques are combined to do so, the approach is also referred to as exploranation. In this context, the audience is usually not required to have domain expertise. However, we show that exploranation can not only support the communication between researchers and a broad audience, but also between researchers directly. With the goal of communicating an existing method for conducting causal inference on spatio-temporal conflict event data, we investigated how to perform exploranation for experts, i.e., expert exploranation. Based on application scenarios of the inference method, we developed three versions of an interactive visual story to explain the method to conflict researchers. We abstracted the corresponding design process and evaluated the stories both with experts who were unfamiliar with the explained method and experts who were already familiar with it. The positive and extensive feedback from the evaluation shows that expert exploranation is a promising direction for visual storytelling, as it can help to improve scientific outreach, methodological understanding, and accessibility for researchers new to a field., Comment: 40 pages, 4 figures, 2 tables

We construct an explicit realization of the action of the $Lw_{1+\infty}$ loop algebra on fields at null infinity. This action is directly derived by Penrose transform of the geometrical action of $Lw_{1+\infty}$ symmetries in twistor space, ensuring that it forms a representation of the algebra. Finally, we show that this action coincides with the canonical action of $Lw_{1+\infty}$ Noether charges on the asymptotic phase space., Comment: 25 pages, 2 figures

How many ways are there to redistrict the $n\times n$ grid into $n$ districts of equal size? How many of these redistricting plans are compact? In this article we give asymptotic bounds on the number of plans, showing there are exponentially many in $n^2$. We then use the lower bound to show that most plans are as least compact as possible., Comment: 11 pages, 11 figures

We review the role that infinite-dimensional symmetries arising at the boundary of asymptotically flat spacetimes play in the context of the celestial holography program. Once recast into the language of conformal field theory, asymptotic symmetries provide key constraints on the sought-for celestial dual to quantum gravity in flat spacetimes., Comment: Invited review for Physics Reports (preprint), 79 pages, 7 figures

We revisit gravitational wave (GW) memory as the key to measuring spacetime symmetries, extending beyond its traditional role in GW searches. In particular, we show how these symmetries may be probed via displacement and spin memory observations, respectively. We further find that the Einstein Telescope's (ET) sensitivity enables constraining the strain amplitude of a displacement memory to 2% and that of spin memory to 22%. Finally, we point out that neglecting memory could lead to an overestimation of measurement uncertainties for parameters of binary black hole (BBH) mergers by about 10% in ET., Comment: 13 pages, 6 figures, 1 table

Soft graviton theorems receive one-loop contributions that are logarithmic in the energy of the soft graviton, and which are closely related to tails of gravitational waveforms. We demonstrate that these logarithmic corrections are encoded in the Ward identity of superrotation symmetries, i.e. they follow from conservation of superrotation charge across spatial infinity $i^0$. Our proof relies on a careful analysis of the radiative phase space admitting such gravitational tails, and the determination of the fluxes through null infinity $\mathscr I$ that act as canonical generators of superrotations on both gravitational and matter fields. All logarithmic terms are derived from the fluxes through correlations of the supertranslation Goldstone mode, provided care is taken in manipulating gravitationally interacting (i.e. dressed) rather than free fields. In cases where massive particles take part in the scattering process, logarithmic corrections also partly arise from the superrotation charge generator at timelike infinity $i^\pm$., Comment: 15 pages

In legislative redistricting, most states draw their House and Senate maps separately. Ohio and Wisconsin require that their Senate districts be made with a 3:1 nesting rule, i.e., out of triplets of adjacent House districts. We seek to study the impact of this requirement on redistricting, specifically on the number of seats won by a particular political party. We compare two ensembles generated using Markov Chain Monte Carlo methods; one which uses the ReCom chain to generate Senate maps without a nesting requirement, and the other which uses a chain that generates Senate maps with a 3:1 nesting requirement. We find that requiring a 3:1 nesting rule has minimal impact on the distribution of seats won. Moreover, we study the impact the chosen House map has on the distribution of nested Senate maps, and find that an extreme seat bias at the House level does not significantly impact the distribution of seats won at the Senate level., Comment: 15 pages, 9 figures. For associated code, see https://github.com/cdonnay/nesting_OH_WI. Submitted to Statistics and Public Policy

We study celestial amplitudes in string theory at one-loop. Celestial amplitudes describe scattering processes of boost eigenstates and relate to amplitudes in the more standard basis of momentum eigenstates through a Mellin transform. They are thus sensitive to both the ultraviolet and the infrared, which raises the question of how to appropriately take the field theory limit of string amplitudes in the celestial basis. We address this problem in the context of four-dimensional genus-one scattering processes of gluons in open string theory which reach the two-dimensional celestial sphere at null infinity. We show that the Mellin transform commutes with the adequate limit in the worldsheet moduli space and reproduces the celestial one-loop field theory amplitude expressed in the worldline formalism. The dependence on $\alpha'$ continues to be a simple overall factor in one-loop celestial amplitudes albeit with a power that is shifted by three units with respect to tree-level, thus making manifest that the dimensionless parameter $g_{10}^2/\alpha'^3$ organizes the loop expansion in the celestial basis., Comment: 23 pages, 1 figure

Gravity in $4d$ asymptotically flat spacetime constitutes the archetypal example of a gravitational system with leaky boundary conditions. Pursuing our analysis of [1], we argue that the holographic description of such a system requires the coupling of the dual theory living at null infinity to some external sources encoding the radiation reaching the conformal boundary and responsible for the non-conservation of the charges. In particular, we show that the sourced Ward identities of a conformal Carrollian field theory living at null infinity reproduce the BMS flux-balance laws. We also derive the general form of low-point correlation functions for conformal Carrollian field theories and exhibit a new branch of solutions, which is argued to be the relevant one for holographic purposes. We then relate our Carrollian approach to the celestial holography proposal by mapping the Carrollian Ward identities to those constraining celestial operators through a suitable integral transform., Comment: 77 pages, 4 figures. Published version in Phys. Rev. D (Editors' Suggestion)

We construct a basis of conformal primary wavefunctions (CPWs) for $p$-form fields in any dimension, calculating their scalar products and exhibiting the change of basis between conventional plane wave and CPW mode expansions. We also perform the analysis of the associated shadow transforms. For each family of $p$-form CPWs, we observe the existence of pure gauge wavefunctions of conformal dimension $\Delta=p$, while shadow $p$-forms of this weight are only pure gauge in the critical spacetime dimension value $D=2p+2$. We then provide a systematic technique to obtain the large-$r$ asymptotic limit near $\mathscr I$ based on the method of regions, which naturally takes into account the presence of both ordinary and contact terms on the celestial sphere. In $D=4$, this allows us to reformulate in a conformal primary language the links between scalars and dual two-forms., Comment: 56 pages + references

The shift of public debate to the digital sphere has been accompanied by a rise in online hate speech. While many promising approaches for hate speech classification have been proposed, studies often focus only on a single language, usually English, and do not address three key concerns: post-deployment performance, classifier maintenance and infrastructural limitations. In this paper, we introduce a new human-in-the-loop BERT-based hate speech classification pipeline and trace its development from initial data collection and annotation all the way to post-deployment. Our classifier, trained using data from our original corpus of over 422k examples, is specifically developed for the inherently multilingual setting of Switzerland and outperforms with its F1 score of 80.5 the currently best-performing BERT-based multilingual classifier by 5.8 F1 points in German and 3.6 F1 points in French. Our systematic evaluations over a 12-month period further highlight the vital importance of continuous, human-in-the-loop classifier maintenance to ensure robust hate speech classification post-deployment., Comment: Findings of EMNLP 2022

We demonstrate that the one-loop exact subleading soft graviton theorem automatically follows from conservation of the BMS charges, provided that the hard and soft fluxes separately represent the extended BMS algebra at null infinity. This confirms that superrotations are genuine symmetries of the gravitational $\mathcal{S}$-matrix beyond the semiclassical regime. In contrast with a previous proposal, the celestial stress-tensor accounting for the one-loop corrections follows from the gravitational phase space analysis and does not require the addition of divergent counterterms. In addition, we show that the symplectic form on the radiative phase space factorises into hard and soft sectors, and that the resulting canonical generators precisely coincide with the correct BMS fluxes., Comment: 20 pages + appendices; v2: added comments; v3: added funding acknowledgment

We consider massless scattering from the point of view of the position, momentum, and celestial bases. In these three languages different properties of physical processes become manifest or obscured. Within the soft sector, they highlight distinct aspects of the infrared triangle: quantum field theory soft theorems arise in the limit of vanishing energy $\omega$, memory effects are described via shifts of fields at the boundary along the null time coordinate $u$, and celestial symmetry algebras are realized via currents that appear at special values of the conformal dimension $\Delta$. We focus on the subleading soft theorems at $\Delta=1-s$ for gauge theory $(s=1)$ and gravity $(s=2)$ and explore how to translate the infrared triangle to the celestial basis. We resolve an existing tension between proposed overleading gauge transformations as examined in the position basis and the `Goldstone-like' modes where we expect celestial symmetry generators to appear. In the process we elucidate various order-of-limits issues implicit in the celestial formalism. We then generalize our construction to the tower of $w_{1+\infty}$ generators in celestial CFT, which probe further subleading-in-$\omega$ soft behavior and are related to subleading-in-$r$ vacuum transitions that measure higher multipole moments of scatterers. In the end we see that the celestial basis is `just right' for identifying the symmetry structure., Comment: 48 pages, 5 figures

We show that a $3d$ sourced conformal Carrollian field theory has the right kinematic properties to holographically describe gravity in $4d$ asymptotically flat spacetime. The external sources encode the leaks of gravitational radiation at null infinity. The Ward identities of this theory are shown to reproduce those of the $2d$ celestial CFT after relating Carrollian to celestial operators. This suggests a new set of interplays between gravity in asymptotically flat spacetime, sourced conformal Carrollian field theory and celestial CFT., Comment: 9 pages, 1 figure, published version (PRL)

Large amounts of annotated data have become more important than ever, especially since the rise of deep learning techniques. However, manual annotations are costly. We propose a tool that enables researchers to create large, high-quality, annotated datasets with only a few manual annotations, thus strongly reducing annotation cost and effort. For this purpose, we combine an active learning (AL) approach with a pre-trained language model to semi-automatically identify annotation categories in the given text documents. To highlight our research direction's potential, we evaluate the approach on the task of identifying frames in news articles. Our preliminary results show that employing AL strongly reduces the number of annotations for correct classification of even these complex and subtle frames. On the framing dataset, the AL approach needs only 16.3\% of the annotations to reach the same performance as a model trained on the full dataset.

Media bias and its extreme form, fake news, can decisively affect public opinion. Especially when reporting on policy issues, slanted news coverage may strongly influence societal decisions, e.g., in democratic elections. Our paper makes three contributions to address this issue. First, we present a system for bias identification, which combines state-of-the-art methods from natural language understanding. Second, we devise bias-sensitive visualizations to communicate bias in news articles to non-expert news consumers. Third, our main contribution is a large-scale user study that measures bias-awareness in a setting that approximates daily news consumption, e.g., we present respondents with a news overview and individual articles. We not only measure the visualizations' effect on respondents' bias-awareness, but we can also pinpoint the effects on individual components of the visualizations by employing a conjoint design. Our bias-sensitive overviews strongly and significantly increase bias-awareness in respondents. Our study further suggests that our content-driven identification method detects groups of similarly slanted news articles due to substantial biases present in individual news articles. In contrast, the reviewed prior work rather only facilitates the visibility of biases, e.g., by distinguishing left- and right-wing outlets.

Slanted news coverage strongly affects public opinion. This is especially true for coverage on politics and related issues, where studies have shown that bias in the news may influence elections and other collective decisions. Due to its viable importance, news coverage has long been studied in the social sciences, resulting in comprehensive models to describe it and effective yet costly methods to analyze it, such as content analysis. We present an in-progress system for news recommendation that is the first to automate the manual procedure of content analysis to reveal person-targeting biases in news articles reporting on policy issues. In a large-scale user study, we find very promising results regarding this interdisciplinary research direction. Our recommender detects and reveals substantial frames that are actually present in individual news articles. In contrast, prior work rather only facilitates the visibility of biases, e.g., by distinguishing left- and right-wing outlets. Further, our study shows that recommending news articles that differently frame an event significantly improves respondents' awareness of bias.

Datasets and methods for cross-document coreference resolution (CDCR) focus on events or entities with strict coreference relations. They lack, however, annotating and resolving coreference mentions with more abstract or loose relations that may occur when news articles report about controversial and polarized events. Bridging and loose coreference relations trigger associations that may lead to exposing news readers to bias by word choice and labeling. For example, coreferential mentions of "direct talks between U.S. President Donald Trump and Kim" such as "an extraordinary meeting following months of heated rhetoric" or "great chance to solve a world problem" form a more positive perception of this event. A step towards bringing awareness of bias by word choice and labeling is the reliable resolution of coreferences with high lexical diversity. We propose an unsupervised method named XCoref, which is a CDCR method that capably resolves not only previously prevalent entities, such as persons, e.g., "Donald Trump," but also abstractly defined concepts, such as groups of persons, "caravan of immigrants," events and actions, e.g., "marching to the U.S. border." In an extensive evaluation, we compare the proposed XCoref to a state-of-the-art CDCR method and a previous method TCA that resolves such complex coreference relations and find that XCoref outperforms these methods. Outperforming an established CDCR model shows that the new CDCR models need to be evaluated on semantically complex mentions with more loose coreference relations to indicate their applicability of models to resolve mentions in the "wild" of political news articles.

Starting from gravity in asymptotically flat spacetime, the BMS momentum fluxes are constructed. These are non-local expressions of the solution space living on the celestial Riemann surface. They transform in the coadjoint representation of the extended BMS group and correspond to Virasoro primaries under the action of bulk superrotations. The relation between the BMS momentum fluxes and celestial CFT operators is then established: the supermomentum flux is related to the supertranslation operator and the super angular momentum flux is linked to the stress-energy tensor of the celestial CFT. The transformation under the action of asymptotic symmetries and the OPEs of the celestial CFT currents are deduced from the BMS flux algebra., Comment: 30 pages, v2: added references

Unsupervised concept identification through clustering, i.e., identification of semantically related words and phrases, is a common approach to identify contextual primitives employed in various use cases, e.g., text dimension reduction, i.e., replace words with the concepts to reduce the vocabulary size, summarization, and named entity resolution. We demonstrate the first results of an unsupervised approach for the identification of groups of persons as actors extracted from a set of related articles. Specifically, the approach clusters mentions of groups of persons that act as non-named entity actors in the texts, e.g., "migrant families" = "asylum-seekers." Compared to our baseline, the approach keeps the mentions of the geopolitical entities separated, e.g., "Iran leaders" != "European leaders," and clusters (in)directly related mentions with diverse wording, e.g., "American officials" = "Trump Administration."

Many people consider news articles to be a reliable source of information on current events. However, due to the range of factors influencing news agencies, such coverage may not always be impartial. Media bias, or slanted news coverage, can have a substantial impact on public perception of events, and, accordingly, can potentially alter the beliefs and views of the public. The main data gap in current research on media bias detection is a robust, representative, and diverse dataset containing annotations of biased words and sentences. In particular, existing datasets do not control for the individual background of annotators, which may affect their assessment and, thus, represents critical information for contextualizing their annotations. In this poster, we present a matrix-based methodology to crowdsource such data using a self-developed annotation platform. We also present MBIC (Media Bias Including Characteristics) - the first sample of 1,700 statements representing various media bias instances. The statements were reviewed by ten annotators each and contain labels for media bias identification both on the word and sentence level. MBIC is the first available dataset about media bias reporting detailed information on annotator characteristics and their individual background. The current dataset already significantly extends existing data in this domain providing unique and more reliable insights into the perception of bias. In future, we will further extend it both with respect to the number of articles and annotators per article.

News is a central source of information for individuals to inform themselves on current topics. Knowing a news article's slant and authenticity is of crucial importance in times of "fake news," news bots, and centralization of media ownership. We introduce Newsalyze, a bias-aware news reader focusing on a subtle, yet powerful form of media bias, named bias by word choice and labeling (WCL). WCL bias can alter the assessment of entities reported in the news, e.g., "freedom fighters" vs. "terrorists." At the core of the analysis is a neural model that uses a news-adapted BERT language model to determine target-dependent sentiment, a high-level effect of WCL bias. While the analysis currently focuses on only this form of bias, the visualizations already reveal patterns of bias when contrasting articles (overview) and in-text instances of bias (article view).

Extensive research on target-dependent sentiment classification (TSC) has led to strong classification performances in domains where authors tend to explicitly express sentiment about specific entities or topics, such as in reviews or on social media. We investigate TSC in news articles, a much less researched domain, despite the importance of news as an essential information source in individual and societal decision making. This article introduces NewsTSC, a manually annotated dataset to explore TSC on news articles. Investigating characteristics of sentiment in news and contrasting them to popular TSC domains, we find that sentiment in the news is expressed less explicitly, is more dependent on context and readership, and requires a greater degree of interpretation. In an extensive evaluation, we find that the state of the art in TSC performs worse on news articles than on other domains (average recall AvgRec = 69.8 on NewsTSC compared to AvgRev = [75.6, 82.2] on established TSC datasets). Reasons include incorrectly resolved relation of target and sentiment-bearing phrases and off-context dependence. As a major improvement over previous news TSC, we find that BERT's natural language understanding capabilities capture the less explicit sentiment used in news articles.

Traditional media outlets are known to report political news in a biased way, potentially affecting the political beliefs of the audience and even altering their voting behaviors. Many researchers focus on automatically detecting and identifying media bias in the news, but only very few studies exist that systematically analyze how theses biases can be best visualized and communicated. We create three manually annotated datasets and test varying visualization strategies. The results show no strong effects of becoming aware of the bias of the treatment groups compared to the control group, although a visualization of hand-annotated bias communicated bias instances more effectively than a framing visualization. Showing participants an overview page, which opposes different viewpoints on the same topic, does not yield differences in respondents' bias perception. Using a multilevel model, we find that perceived journalist bias is significantly related to perceived political extremeness and impartiality of the article.

We define and study asymptotic Killing and conformal Killing vectors in $d$-dimensional Minkowski, (A)dS, $\mathbb{R}\times S^{d-1}$ and ${\rm AdS}_2\times S^{d-2}$. We construct the associated quantum charges for an arbitrary CFT and show they satisfy a closed algebra that includes the BMS as a sub-algebra (i.e. supertranslations and superrotations) plus a novel transformation we call `superdilations'. We study representations of this algebra in the Hilbert space of the CFT, as well as the action of the finite transformations obtained by exponentiating the charges. In the context of the AdS/CFT correspondence, we propose a bulk holographic description in semi-classical gravity that reproduces the results obtained from CFT computations. We discuss the implications of our results regarding quantum hairs of asymptotically flat (near-)extremal black holes., Comment: 55 pages, v2 updated to match published version

We investigate whether supertranslation symmetry may appear in a scenario that involves black holes in AdS space. The framework we consider is massive 3D gravity, which admits a rich black hole phase space, including stationary AdS black holes with softly decaying hair. We consider a set of asymptotic conditions that permits such decaying near the boundary, and which, in addition to the local conformal symmetry, is preserved by an extra local current. The corresponding algebra of diffeomorphisms consists of two copies of Virasoro algebra in semi-direct sum with an infinite-dimensional Abelian ideal. We then reorient the analysis to the near horizon region, where infinite-dimensional symmetries also appear. The supertranslation symmetry at the horizon yields an infinite set of non-trivial charges, which we explicitly compute. The zero-mode of these charges correctly reproduces the black hole entropy. In contrast to Einstein gravity, in the higher-derivative theory subleading terms in the near horizon expansion contribute to the near horizon charges. Such terms happen to capture the higher-curvature corrections to the Bekenstein area law., Comment: 25 pages, 1 figure

We provide a unified treatment of conformally soft Goldstone modes which arise when spin-one or spin-two conformal primary wavefunctions become pure gauge for certain integer values of the conformal dimension $\Delta$. This effort lands us at the crossroads of two ongoing debates about what the appropriate conformal basis for celestial CFT is and what the asymptotic symmetry group of Einstein gravity at null infinity should be. Finite energy wavefunctions are captured by the principal continuous series $\Delta\in 1+i\mathbb{R}$ and form a complete basis. We show that conformal primaries with analytically continued conformal dimension can be understood as certain contour integrals on the principal series. This clarifies how conformally soft Goldstone modes fit in but do not augment this basis. Conformally soft gravitons of dimension two and zero which are related by a shadow transform are shown to generate superrotations and non-meromorphic diffeomorphisms of the celestial sphere which we refer to as shadow superrotations. This dovetails the Virasoro and Diff(S$^2$) asymptotic symmetry proposals and puts on equal footing the discussion of their associated soft charges, which correspond to the stress tensor and its shadow in the two-dimensional celestial CFT., Comment: 29 pages + appendices, 3 figures

We show that the geometry of a black hole horizon can be described as a Carrollian geometry emerging from an ultra-relativistic limit where the near-horizon radial coordinate plays the role of a virtual velocity of light tending to zero. We prove that the laws governing the dynamics of a black hole horizon, the null Raychaudhuri and Damour equations, are Carrollian conservation laws obtained by taking the ultra-relativistic limit of the conservation of an energy-momentum tensor; we also discuss their physical interpretation. We show that the vector fields preserving the Carrollian geometry of the horizon, dubbed Carrollian Killing vectors, include BMS-like supertranslations and superrotations and that they have non-trivial associated conserved charges on the horizon. In particular, we build a generalization of the angular momentum to the case of non-stationary black holes. Finally, we discuss the relation of these conserved quantities to the infinite tower of charges of the covariant phase space formalism., Comment: 20 pages, 1 figure. Corrected typos

It has recently been shown that, in the vicinity of their event horizons, black holes exhibit an infinite-dimensional symmetry. This symmetry captures relevant physical information about the black hole, and in particular about its thermodynamics. Here, we show that the same holds in a cosmological setup. More precisely, we show that around the de Sitter cosmological horizon, an infinite set of diffeomorphisms preserving a sensible set of boundary conditions emerges. These boundary conditions are similar to those considered by Price and Thorne in the context of the membrane paradigm, and permit to accommodate interesting gravity solutions. As for other boundary conditions considered previously, they are preserved by an infinite-dimensional asymptotic isometry algebra that includes supertranslations and two copies of the Virasoro algebra. This symmetry has associated a set of Noether charges that turn out to be conserved, finite, and integrable. We derive these charges explicitly using the covariant formalism and analyze their physical meaning by evaluating them to the case of de Sitter space. In this case, the zero-mode of the charge is found to account for the Gibbons-Hawking entropy of the cosmological horizon. We then consider a much more general set of solutions, including asymptotically de-Sitter black holes and asymptotically Taub-NUT-de Sitter black holes., Comment: 20 pages, 1 figure

For $A \subseteq \{1,2,\ldots\}$, we consider $R(A) = \{a/a' : a,a' \in A\}$. If $A$ is the set of nonzero values assumed by a quadratic form, when is $R(A)$ dense in the $p$-adic numbers? We show that for a binary quadratic form $Q$, $R(A)$ is dense in $\mathbb{Q}_{p}$ if and only if the discriminant of $Q$ is a nonzero square in $\mathbb{Q}_{p}$, and for a quadratic form in at least three variables, $R(A)$ is always dense in $\mathbb{Q}_{p}$. This answers a question posed by several authors in 2017., Comment: 14 pages

The four-dimensional $S$-matrix is reconsidered as a correlator on the celestial sphere at null infinity. Asymptotic particle states can be characterized by the point at which they enter or exit the celestial sphere as well as their $SL(2,\mathbb C)$ Lorentz quantum numbers: namely their conformal scaling dimension and spin $h\pm \bar h$ instead of the energy and momentum. This characterization precludes the notion of a soft particle whose energy is taken to zero. We propose it should be replaced by the notion of a conformally soft particle with $h=0$ or $\bar h=0$. For photons we explicitly construct conformally soft $SL(2,\mathbb C)$ currents with dimensions $(1,0)$ and identify them with the generator of a $U(1)$ Kac-Moody symmetry on the celestial sphere. For gravity the generator of celestial conformal symmetry is constructed from a $(2,0)$ $SL(2,\mathbb C)$ primary wavefunction. Interestingly, BMS supertranslations are generated by a spin-one weight $(\frac{3}{2},\frac{1}{2})$ operator, which nevertheless shares holomorphic characteristics of a conformally soft operator. This is because the right hand side of its OPE with a weight $(h,\bar h)$ operator ${\cal O}_{h,\bar h}$ involves the shifted operator ${\cal O}_{h+\frac{1}{2},\bar h+ \frac{1}{2}}$. This OPE relation looks quite unusual from the celestial CFT$_2$ perspective but is equivalent to the leading soft graviton theorem and may usefully constrain celestial correlators in quantum gravity., Comment: 23 pages, 1 figure; corrected typos, added references

We compute the memory effect produced at the black hole horizon by a transient gravitational shockwave. As shown by Hawking, Perry, and Strominger (HPS) such a gravitational wave produces a deformation of the black hole geometry which from future null infinity is seen as a Bondi-Metzner-Sachs (BMS) supertranslation. This results in a diffeomorphic but physically distinct geometry which differs from the original black hole by their charges at infinity. Here we give the complementary description of this physical process in the near-horizon region as seen by an observer hovering just outside the event horizon. From this perspective, in addition to a supertranslation the shockwave also induces a horizon superrotation. We compute the associated superrotation charge and show that its form agrees with the one obtained by HPS at infinity. In addition, there is a supertranslation contribution to the horizon charge, which measures the entropy change in the process. We then turn to electrically and magnetically charged black holes and generalize the near-horizon asymptotic symmetry analysis to Einstein-Maxwell theory. This reveals an additional infinite-dimensional current algebra that acts non-trivially on the horizon superrotations. Finally, we generalize the black hole memory effect to Reissner-Nordstr\"{o}m black holes., Comment: 21 pages, 1 figure

We give a new proof of the existence of compact surfaces embedded in $R^3$ with Anosov geodesic flows. This proof starts with a non-compact model surface whose geodesic flow is shown to be Anosov using a uniformly strictly invariant cone condition. Using a sequence of explicit maps based on the standard torus embedding, we produce compact embedded surfaces that can be seen as small perturbations of the Anosov model system and hence are themselves Anosov.

Every quadratic form represents 0; therefore, if we take any number of quadratic forms and ask which integers are simultaneously represented by all members of the collection, we are guaranteed a nonempty set. But when is that set more than just the "trivial" 0? We address this question in the case of integral, positive- definite, reduced, binary quadratic forms. For forms of the same discriminant, we can use the structure of the underlying class group. If, however, the forms have different discriminants, we must apply class field theory.

We introduce the notion of positive local combinatorial dividing-lines in model theory. We show these are equivalently characterized by indecomposable algebraically trivial Fraisse classes and by complete prime filter classes. We exhibit the relationship between this and collapse-of-indiscernibles dividing-lines. We examine several test cases, including those arising from various classes of hypergraphs., Comment: 35 pages

We prove that non-extremal black holes in four-dimensional general relativity exhibit an infinite-dimensional symmetry in their near horizon region. By prescribing a physically sensible set of boundary conditions at the horizon, we derive the algebra of asymptotic Killing vectors, which is shown to be infinite-dimensional and includes, in particular, two sets of supertranslations and two mutually commuting copies of the Virasoro algebra. We define the surface charges associated to the asymptotic diffeomorphisms that preserve the boundary conditions and discuss the subtleties of this definition, such as the integrability conditions and the correct definition of the Dirac brackets. When evaluated on the stationary solutions, the only non-vanishing charges are the zero-modes. One of them reproduces the Bekenstein-Hawking entropy of Kerr black holes. We also study the extremal limit, recovering the NHEK geometry. In this singular case, where the algebra of charges and the integrability conditions get modified, we find that the computation of the zero-modes correctly reproduces the black hole entropy. Furthermore, we analyze the case of three spacetime dimensions, in which the integrability conditions notably simplify and the field equations can be solved analytically to produce a family of exact solutions that realize the boundary conditions explicitly. We examine other features, such as the form of the algebra in the extremal limit and the relation to other works in the literature., Comment: 24 pages, minor corrections

These are the lectures notes of the course given at the Eleventh Modave Summer School in Mathematical Physics, 2015, aimed at PhD candidates and junior researchers in theoretical physics. We review in details the result of Coussaert-Henneaux-van Driel showing that the asymptotic dynamics of $(2+1)$- dimensional gravity with negative cosmological constant is described at the classical level by Liouville theory. Boundary conditions implement the asymptotic reduction in two steps: the first set reduces the $SL(2,\mathbb R)\times SL(2,\mathbb R)$ Chern-Simons action, equivalent to the Einstein action, to a non-chiral $SL(2,\mathbb R)$ Wess-Zumino-Witten model, while the second set imposes constraints on the WZW currents that reduce further the action to Liouville theory. We discuss the issues of considering the latter as an effective description of the dual conformal field theory describing AdS$_3$ gravity beyond the semi-classical regime., Comment: 36 pages, 2 figures. Lecture notes prepared for the Eleventh Modave Summer School in Mathematical Physics, September 2015, Belgium

We show that the asymptotic symmetries close to nonextremal black hole horizons are generated by an extension of supertranslations. This group is generated by a semidirect sum of Virasoro and Abelian currents. The charges associated with the asymptotic Killing symmetries satisfy the same algebra. When considering the special case of a stationary black hole, the zero mode charges correspond to the angular momentum and the entropy at the horizon., Comment: 6 pages, references added, published version

We use the notion of collapse of generalized indiscernible sequences to classify various model theoretic dividing lines. In particular, we use collapse of n-multi-order indiscernibles to characterize op-dimension n; collapse of function-space indiscernibles (i.e. parameterized equivalence relations) to characterize rosy theories; and finally, convex equivalence relation indiscernibles to characterize NTP2 theories., Comment: 18 pages

In a previous paper, it has been shown that the entropy of non-extremal black holes in Warped Anti-de Sitter (WAdS) spaces in massive gravity can be computed microscopically in terms of a dual conformal field theory. Here, we extend this computation to a set of asymptotic boundary conditions that, while still gathering the WAdS$_3$ black holes, also allow for new solutions that are not locally equivalent to WAdS$_3$ space, and therefore are associated to the local degrees of freedom of the theory (bulk massive gravitons). After presenting explicit examples of such geometries, we compute the asymptotic charge algebra and show that it is generated by the semi-direct sum of Virasoro algebra and an affine Kac-Moody algebra. The value of the central charge turns out to be exactly the one that leads to reproduce the entropy of the WAdS$_3$ black holes. This result probes the WAdS$_3$/CFT$_2$ correspondence in presence of bulk gravitons., Comment: 8 pages, 1 figure. Contribution to the Proceedings of the Fourteenth Marcel Grossmann Meeting, Rome, July 12-18, 2015

The two-dimensional super-BMS$_{3}$ invariant theory dual to three-dimensional asymptotically flat $\mathcal{N}=1$ supergravity is constructed. It is described by a constrained or gauged chiral Wess-Zumino-Witten action based on the super-Poincar\'e algebra in the Hamiltonian, respectively the Lagrangian formulation, whose reduced phase space description corresponds to a supersymmetric extension of flat Liouville theory., Comment: 11 pages

We study the asymptotic symmetries of three-dimensional Warped Anti-de Sitter (WAdS) spaces in three-dimensional New Massive Gravity (NMG). For a specific choice of asymptotic boundary conditions, we find that the algebra of charges is infinite-dimensional and coincides with the semidirect sum of Virasoro algebra with non-vanishing central charge and an affine $\hat{u}(1)_k$ Ka\v{c}-Moody algebra. We show that the WAdS black hole configurations organize in terms of two commuting Virasoro algebras. We identify the Virasoro generators that expand the associated representations in the dual Warped Conformal Field Theory (WCFT) and, by applying the Warped version of the Cardy formula, we prove that the microscopic WCFT computation exactly reproduces the entropy of black holes in WAdS space., Comment: 13 pages. v2 minor typos corrected

We consider the timelike version of Warped Anti-de Sitter space (WAdS), which corresponds to the three-dimensional section of the G\"{o}del solution of four-dimensional cosmological Einstein equations. This geometry presents closed timelike curves (CTCs), which are inherited from its four-dimensional embedding. In three dimensions, this type of solutions can be supported without matter provided the graviton acquires mass. Here, among the different ways to consistenly give mass to the graviton in three dimensions, we consider the parity-even model known as New Massive Gravity (NMG). In the bulk of timelike WAdS$_{3}$ space, we introduce defects that, from the three-dimensional point of view, represent spinning massive particle-like objects. For this type of sources, we investigate the definition of quasi-local gravitational energy as seen from infinity, far beyond the region where the CTCs appear. We also consider the covariant formalism applied to NMG to compute the mass and the angular momentum of spinning particle-like defects, and compare the result with the one obtained by means of the quasi-local stress-tensor. We apply these methods to special limits in which the WAdS$_3$ solutions coincide with locally AdS$_3$ and locally AdS$_{2}\times \mathbb{R}$ spaces. Finally, we make some comments about the asymptotic symmetry algebra of asymptotically WAdS$_3$ spaces in NMG., Comment: 16 pages, published version

The dS/CFT correspondence postulates the existence of a Euclidean CFT dual to a suitable gravity theory with Dirichlet boundary conditions asymptotic to de Sitter spacetime. A semi-classical model of such a correspondence consists of Einstein gravity with positive cosmological constant and without matter which is dual to Euclidean Liouville theory defined at the future conformal boundary. Here we show that Euclidean Liouville theory is also dual to Einstein gravity with Dirichlet boundary conditions on a fixed timelike slice in the static patch. Intriguingly, the spacetime interpretation of Euclidean Liouville time is the physical time of the static observer. As a prerequisite of this correspondence, we show that the asymptotic symmetry algebra which consists of two copies of the Virasoro algebra extends everywhere into the bulk., Comment: 19 pages

A consistent set of asymptotic conditions for the simplest supergravity theory without cosmological constant in three dimensions is proposed. The canonical generators associated to the asymptotic symmetries are shown to span a supersymmetric extension of the BMS$_3$ algebra with an appropriate central charge. The energy is manifestly bounded from below with the ground state given by the null orbifold or Minkowski spacetime for periodic, respectively antiperiodic boundary conditions on the gravitino. These results are related to the corresponding ones in AdS$_3$ supergravity by a suitable flat limit. The analysis is generalized to the case of minimal flat supergravity with additional parity odd terms for which the Poisson algebra of canonical generators form a representation of the super-BMS$_3$ algebra with an additional central charge., Comment: 13 pages, no figures

We discuss models and data of crowd disasters, crime, terrorism, war and disease spreading to show that conventional recipes, such as deterrence strategies, are often not effective and sufficient to contain them. Many common approaches do not provide a good picture of the actual system behavior, because they neglect feedback loops, instabilities and cascade effects. The complex and often counter-intuitive behavior of social systems and their macro-level collective dynamics can be better understood by means of complexity science. We highlight that a suitable system design and management can help to stop undesirable cascade effects and to enable favorable kinds of self-organization in the system. In such a way, complexity science can help to save human lives., Comment: 67 pages, 25 figures; accepted for publication in Journal of Statistical Physics [for related work see http://www.futurict.eu/]

Containing the spreading of crime is a major challenge for society. Yet, since thousands of years, no effective strategy has been found to overcome crime. To the contrary, empirical evidence shows that crime is recurrent, a fact that is not captured well by rational choice theories of crime. According to these, strong enough punishment should prevent crime from happening. To gain a better understanding of the relationship between crime and punishment, we consider that the latter requires prior discovery of illicit behavior and study a spatial version of the inspection game. Simulations reveal the spontaneous emergence of cyclic dominance between ''criminals'', ''inspectors'', and ''ordinary people'' as a consequence of spatial interactions. Such cycles dominate the evolutionary process, in particular when the temptation to commit crime or the cost of inspection are low or moderate. Yet, there are also critical parameter values beyond which cycles cease to exist and the population is dominated either by a stable mixture of criminals and inspectors or one of these two strategies alone. Both continuous and discontinuous phase transitions to different final states are possible, indicating that successful strategies to contain crime can be very much counter-intuitive and complex. Our results demonstrate that spatial interactions are crucial for the evolutionary outcome of the inspection game, and they also reveal why criminal behavior is likely to be recurrent rather than evolving towards an equilibrium with monotonous parameter dependencies., Comment: 9 two-column pages, 5 figures; accepted for publication in PLoS ONE

In this paper, we build a dimension theory related to Shelah's 2-rank, dp-rank, and o-minimal dimension. We call this dimension op-dimension. We exhibit the notion of the n-multi-order property, generalizing the order property, and use this to create op-rank, which generalizes 2-rank. From this we build op-dimension. We show that op-dimension bounds dp-rank, that op-dimension is sub-additive, and op-dimension generalizes o-minimal dimension in o-minimal theories., Comment: 30 pages

We demonstrate that for the $k$-variable theory $T$ of a finite structure (satisfying certain amalgamation conditions), if finite models of $T$ can be recovered from diagrams of finite {\em subsets} of model of $T$ in a certain "efficient" way, then $T$ is rosy -- in fact, a certain natural $\aleph_0$-categorical completion $T^{\lim}$ of $T$ is super-rosy of finite $U^\thorn$-rank. In an appendix, we also show that any $k$-variable theory $T$ of a finite structure for which the Strong $L^k$-Canonization Problem is efficient soluble has the necessary amalgamation properties up to taking an appropriate reduct., Comment: 24 pages